Here, the momentum dependence of \(\tau _R\)  is expressed as a power law of \(\tilde{E}_{\text{p}}\)  in the comoving frame, with \(\tau _R^0\)  as the momentum independent part; the parameter \(\Lambda \)  specify the power of the scaled energy.
By the virtue of collision operator properties, the right hand side of Eq. (REF ) retains only the interaction part of \(\phi \) , since it is the sole part that can be determined
from the transport equation.
To solve Eq. (REF ), we adopt the well-known iterative technique of gradient expansion given by Chapman-Enskog (CE) [1]}. Employing that, the inhomogeneous or interaction part of the first-order out-of-equilibrium distribution function from Eq. (REF ) turns out to be,
\(&\phi _{\text{int}}^{(1)}=-\tau _R^0\tilde{E}_{\text{p}}^{\Lambda -1}\bigg [\tilde{E}_{\text{p}}^2\frac{DT}{T}+\tilde{E}_{\text{p}} D\tilde{\mu }+\left(\frac{\tilde{E}_{\text{p}}^2}{3}-\frac{z^2}{3}\right)(\partial \cdot u)\nonumber \\&+\tilde{E}_{\text{p}}\tilde{p}^{\langle \mu \rangle }\left(\frac{\nabla _{\mu }T}{T}-Du_{\mu }\right)+\tilde{p}^{\langle \mu \rangle }\nabla _{\mu }\tilde{\mu }-\tilde{p}^{\langle \mu }\tilde{p}^{\nu \rangle }\sigma _{\mu \nu }\bigg ],\) 
